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CHAPTER5
CombinationalLogicAnalysisandDesign(组合逻辑电路分析和设计)组合逻辑电路时序逻辑电路components:LogicGatesCombinationallogiccircuitSequentiallogiccircuitcomponents:LogicGates+FlipFlops,LatchesChapter7,8,9,10Chapter5,6theoutputisonlydependedonthecurrentinputsTheoutputisnotonlydependedonthecurrentinputsbutalsodependedonthepaststateCombinationallogiccircuitchapter5chapter6CombinationallogicAnalysisandDesignFunctionsofcombinationalLogic5-1BasicCombinationalLogicCircuits5-2CombinationalLogicCircuits
Analysis5-3ImplementingCombinationalLogic
5-4TheUniversalPropertyofNANDandNORGates
5-5CombinationalLogicUsingNANDandNORGates5-6LogicCircuitOperationWithPulseWaveformCHAPTER5CombinationalLogicAnalysisandDesignAND-ORLogic(与-或逻辑电路)AND-OR-InvertLogic(与-或-非逻辑电路)Exclusive-ORLogic(异-或逻辑电路)5-1BasicCombinationalLogicCircuitsAND-ORLogicTruthtableINPUTSABCDABCDOUTPUTX0000000100100011010001010110011110001001101010111100110111101111000000010000000100000001101010110001000100011111XX=AB+CDAND-ORLogicAND-ORInvertLogicExclusive-ORLogicABX000110110110TruthtableExclusive-NORLogic
BooleanexpressionTruthtableTwoequivalentwaysofimplementingtheexclusive-NOR
Samelogiccanbeimplementedbydifferentcircuit5-2CombinationalLogicCircuitsAnalysis
(组合逻辑电路分析)LogicCircuitLogicFunctionX=F(A,B,C)?ThesensorproduceaHIGHwhenthelevelofchemicalinthetankdropsbelowaspecifiedpointBCABACA,B,Carelevelsensors.aHIGHisproducedwhenthelevelofchemicalinthetankdropsbelowaspecifiedpoint.AnalysisthefunctionofthecircuitX=AB+BC+ACBCABACX=AB+BC+ACTruthtableABCABBCACX00000101001110010111011100000000001000000110011100010111Thelow-levelindicatorwillgiveanindicationwhenmorethantwotanks’leveldropbelowthespecifiedpoint!AnalysisthefunctionofthecircuitAnalysisthefunctionofthecircuit(review)
Step1:ObtaintheLogicExpressionfromthelogiccircuitStep2:ConstructingaTruthTablefortheLogiccircuitStep3:Analysisthefunction
5-3ImplementingCombinationalLogic
(组合逻辑电路的设计)LogicCircuitLogicFunction1.FromanapplicationtoaTruthTable2.FromaTruthTabletoasimplifiedlogicexpression3.FromthesimplifiedlogicexpressiontoalogiccircuitExample:Implementavotingcircuitforthreeperson.Eachpersonhasonebutton.Pressthebuttonforagreementandleaveitfordisagreement.TheoutputwillshowonaLEDlight.Thelightonwhenmajoritypeopleagreed.Otherwise,thelightoff.三人表决电路每人一个按键,如果同意则按下,不同意则不按。结果用指示灯表示,多数同意时指示灯亮,否则不亮。FromlogicfunctiontoTruthTableTruthTableInputs:A、B、CAgree“1”,otherwise“0”Output:FLighton“1”,otherwise“0”Implementavotingcircuitforthreeperson(A、B、C):
Eachpersonhasonebuttoninfrontofhim.Pressthebuttonforagreementandleaveitfordisagreement.
TheoutputwillshowonaLEDlight.Thelightonwhenmajoritypeopleagreed.Otherwise,lightoff.
TruthTable2.FromTruthTabletosimplifiedlogicexpressionABC0001111001ABACBCABBCCAF3.FromLogicExpressiontoLogicCircuitAnd-OrLogic3.FromLogicExpressiontoLogicCircuitchap5-1a.ewbImplementathreeinputsparitychecker:Theoutputis“1”whenthenumberofinput“1”isodd.
(1)TruthTable
(2)Logicexpression
0000
A
B
C
Y0011010101101001101011001111ABC00100111101111Solution:奇偶检验器
(3)logiccircuit
(3)logiccircuitChap5奇偶校验电路.ewbstep1.FromanapplicationtoaTruthTablestep2.FromaTruthTabletoasimplifiedlogicexpressionstep3.FromthesimplifiedlogicexpressiontoalogiccircuitCombinationLogicImplementation(Review)LogicCircuitLogicFunctionTextbook:Page168ch5-25-3TheUniversalProperty
ofNANDandNORGates
NANDandNORgatesare“universal”becausetheycanusedtoproduceanyoftheotherlogicfunctionsTheNANDGateasaUniversalLogicElementTheNORGateasaUniversalLogicElementNANDGateasanInverterTheNANDGateasaUniversalLogicElement?AAHIGH??NANDGateasanInverterxTwoNANDGatesasanANDGate?ThreeNANDGatesasanORGateFourNANDGatesasNORGateFourNANDGatesasXORGateNORGateasanInverterTheNORGateasaUniversalLogicElementTwoNORGatesasanORGateThreeNORGatesasanANDGateFourNORGatesasanNANDGateNANDlogicforX=AB+CD?5-4COMBINATIONALLOGICUSINGNANDANDNORGATEDeMorgan’s最简逻辑电路标准门的个数最少每个门的连线最少门的种类最少
NANDLogicDiagramsUsingDualsymbolswhendrawingaNANDlogicdiagram,alwaysusethegatesymbolsinsuchawaythateveryconnectionbetweenagateoutputandagateinputiseitherbubble-to-bubbleornonbubble-to-nonbubble.UseoftheappropriatedualsymbolsinaNANDlogicdiagrameveryconnectionbetweenagateoutputandagateinputiseitherbubble-to-bubbleornonbubble-to-nonbubbleEXAMPLE:ImplementeachexpressionwithNANDlogicusingappropriatedualsymbols(a)EXAMPLE:ImplementeachexpressionwithNANDlogicusingappropriatedualsymbols(b)NORLOGICNORnegative-ANDNORlogicforX=(A+B)(C+D)
ANORgatefunctionaseitheraNORoranegative-AND.180三人表决电路:
Implementavotingcircuitforthreeperson(A、B、C):UseNANDgatesABCAnd-OrLogicGatesABCNANDLogicGates最简逻辑电路标准门的个数最少每个门的连线最少门的种类最少Implementathreeinputsparitychecker:Theoutputis“1”whenthenumberofinput“1”isodd.奇偶检验器(3)ConverttoNANDlogic
(2)LogicexpressionUseNANDGates!EX5-12:DeterminethefinaloutputwaveformXforthecircuit,withinputwaveformsA,BandCasshown.5-5CIRCUITOPERATIONWITHPULSEWAVEFORMINPUTSEX5-11:DrawthetimingdiagramFindoutthelogiccircuitthatwillgeneratetheoutputwaveformfortheinputs.inputsoutputABCX000Page193:Problem30Homework:Page193Problem31DigitalSystemApplication7-segmentdisplayspage149共阳极接法共阴极接法gfedcba例:共阴极接法a
b
c
d
e
f
g
01100001101101低电平时发光高电平时发光共阳极接法abcgdef+dgfecbag共阴极接法abcdefg二-十进制编码?显示器件
D
C
BAa
b
c
d
efg00001111110000010110000100101101101200111111001301000110011401011011011501101011111601111110000710001111111810011
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